Recently finished The Emperor's New Mind by Roger Penrose, an Oxford physicist. According to Penrose, the action of the brain is fundamentally different from and cannot, even in principle, be reduced to the working of a deterministic computer. The argument is one I have some sympathy for, though I'm not sure Penrose makes his case completely convincing. Even so, the book is a fascinating trip through issues of computability, determinism, and the mind-body problem that I hadn't considered before.
Most physical laws are deterministic, which means that given the state of a system at one time you can, at least in principle, predict its state for the entire future. But at the quantum level things are a little bit more tricky and certain things (the position of an electron, say) are observed to behave probabilistically. Though most physicists and biologists would argue that quantum effects are not important at the level of human brains, Penrose disagrees and sees this as an opening for the presence of conciousness and free will.
Now may be as good a time as any to reveal that I've started my own blog. I hope no one's offended; it has a different kind of feel from the Crawdad Hole, and I will continue to post here from time to time as I have things to say that seem to fit better here than there.
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